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Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations - On Sharpness of J.-L. Lions Exponent

Tianwen Luo Tsinghua University Edriss S. Titi Texas A\&M University; University of Cambridge; The Weizmann Institute of Science

Analysis of PDEs mathscidoc:1906.03008

Using the convex integration technique for the three-dimensional Navier-Stokes equations introduced by T. Buckmaster and V. Vicol, it is shown the existence of non-unique weak solutions for the 3D Navier-Stokes equations with fractional hyperviscosity $(-\Delta)^{\theta}$, whenever the exponent $\theta$ is less than J.-L. Lions' exponent $5/4$, i.e., when $\theta < 5/4$.
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@inproceedings{tianwennon-uniqueness,
  title={Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations - On Sharpness of J.-L. Lions Exponent},
  author={Tianwen Luo, and Edriss S. Titi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190628071642873212380},
}
Tianwen Luo, and Edriss S. Titi. Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations - On Sharpness of J.-L. Lions Exponent. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190628071642873212380.
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